Intelligent Design is a theory of beginnings that views the complexity and order of the Universe as evidence that things were made on purpose (e.g. by a "designer"), not by random chance (as is assumed by Darwinism).
Evolutionary theory, in contrast, proposes that our Universe began apart from any intention or intelligence - that a "big bang" or similar event brought into existence all matter and energy accidentally, and that natural laws and processes can explain our existence.
Typically Intelligent Design is distinguished from "creationism," which is a religious understanding of beginnings. While many intelligent design theorists are also creationists, the two are not intrinsically related. Intelligent design theory seeks truth regarding the history of the world based on observable data -- not based on religious conviction.
(Full disclosure: I'm an Intelligent Design proponent, and I also happen to be a creationist. Surprise, surprise.)
Does evidence exist for intelligent design?
Absolutely. However, one must understand that each set of scientists (Darwinists or Intelligent Design Proponents) are looking at the same evidence -- it is a matter of the interpretation. Evolutionists filter the evidence they see through their assumptions about random chance creating the universe; intelligent design theorists filter the evidence they see through their assumption that a purposeful being made or guided the formation of the universe. Good evidences (such as irreducible complexity) have been presented indicating a designer must have been involved in the creation of life. Such evidence can be studied in detail in the book "Defeating Darwinism by Opening Minds" by Phillip Johnson.
Evolutionists will often say that "no scientific evidence exists to support intelligent design", but it must be clearly understood that such statements are not rooted in fact, but rather opinion. Because these people don't believe in the possibility of an intelligent designer, they are unwilling to see that any evidence could support such a being. This only proves again that evolution, too, is based on presuppositions, not empirical data.
(Note: watch what happens when evidence does arise that would naturally lead someone to conclude a designer was behind the universe. Rather than address the evidence itself, Darwinists are likely to "define" science in such a way as to exclude that evidence from consideration. In other words, "since the idea of a designer is outside the realm of science, we must..." This is a clever way of keeping the upper hand in the debate and never actually answering critics.)
Why does it really matter? Aren't we just splitting hairs over this?
The desperate attempts of evolutionists to crackdown on academic freedom and keep the evidence for intelligent design under the radar shows how important evolution is to their philosophy of life. (Evolutionary philosophy assumes that life is meaningless and that there is no ultimate moral accountability.) On the other hand, intelligent design is also used as the basis for a philosophy of life (this philosophy states that life has meaning, guidelines, and purpose as determined by the designer).
It matters because, in a personal sense, we won't know who we are or where we are going unless we can get a clear picture of where we came from (and why, if that question proves to be valid). What are we as human beings? Accidental? Purposeful? Animal? Important? Temporal? Eternal? The answers begin at the beginning.